This drawback motivates the weak form of SINDy [1]}, [2]}, [3]} (which also generalizes to the PDE case [4]}, [5]}), where both sides of Equation REF  are integrated over a random collection of \(K\)  temporal subdomains (spatiotemporal for PDEs). That is, for a random subdomain \(\Omega _k\) , a candidate library function \(\mathbf {f}_i\) , and a weight vector \(\mathbf {w}\) , we compute
\( q_i^k = \int _{\Omega _k} \mathbf {w}^T \mathbf {f}_i d\Omega \) 
